Epistemic and Doxastic Contents

The case for making belief states the primary focus of our analysis and for including impossible worlds in that analysis is outlined in this chapter. This allows the reader to deny various closure principles, although this won’t help defeat worries about external-world scepticism. The issue that concerns the authors most is the problem of bounded rationality: belief states seem to be closed under ‘easy’ trivial consequence, but not under full logical consequence, and yet the former implies the latter. The solution presented here is that some trivial closure principle must fail on a given belief state, yet it is indeterminate just where this occurs. Formal models of belief states along these lines are given and it is shown that they respect the indeterminacy-of-closure intuition. Finally, the chapter discusses how we might square this approach with the fact that some people seem to believe contradictions.

The Logic of Imagination

Imagination seems to have a logic, albeit one which is hyperintensional and sensitive to context. This chapter offers a semantics of imagination, with operators expressing ‘imaginative acts’ of mental simulation. A number of conditions that could be imposed on the semantics are then discussed, in order to validate certain inferences. One important issue is how acts of imagination interact with disjunction: one can imagine some disjunction as obtaining without being imaginatively specific about which disjunction obtains. This chapter subsequently turns to non-monotonicity: how B may follow from imagining that A, but not from imagining that A ∧ C. Finally, the Principle of Imaginative Equivalents is discussed.

Relevant Logics

Relevant logics aim to avoid the ‘paradoxes’ of the material and strict conditionals. Their most natural semantics, the Routley-Meyer semantics, is given in terms of impossible worlds. By placing certain further conditions on those worlds, we can obtain stronger relevant logics. One of the main philosophical issues surrounding the general approach concerns how to interpret the Routley-Meyer ternary relation on worlds and the Routley star. The information-theoretic interpretation has proved popular but, it is argued, it faces philosophical issues. An alternative interpretation takes its cue from ways of thinking about conditionality in general. The three options are considered, but issues are found with each of them. A final option is the truthmaker interpretation of relevant logics, which is promising but under-developed.

Fiction and Fictional Objects

This chapter begins with the problem of what counts as true in a given fiction, beyond what’s explicitly given in that fiction. It then considers the problem of inconsistent fictions, which are naturally handled using impossible worlds. An account of truth in fiction is presented, which develops one of Lewis’s analyses into an approach which can handle inconsistent fictions with ease. The chapter then turns to the second main topic: how we should think about fictional entities. Realism and fictionalism about fictional characters are contrasted. A third option is then considered, which takes the Meinongian line that fictional characters are non-existent objects. Several versions of this idea and their various issues are discussed.

Information and Content

This chapter conceptualizes information in terms of ruling out scenarios. It discusses informative identity statements, which give rise to Frege’s puzzle, and the problem understanding how a valid logical inference can be informative. An analysis of informative logical inferences is given, on which the content of a valid deduction is often indeterminate. A consequence is that it is indeterminate exactly which logical inferences are informative. The chapter then analyses a rather different notion of content, concerning what is said by a speaker in making an utterance.

Counterpossible Conditionals

Vacuism is the view that all counterpossibles are trivially true. There are reasons to think it incorrect. An impossible worlds semantics for counterfactuals is offered, which makes room for non-trivial counterpossibles. One principle which pins down its application is the Strangeness of Impossibility condition: for any given possible world, any impossible worlds is further away from it than any possible world is. A number of Williamson’s objections to the non-vacuist approach are discussed and it is argued that they can be overcome. The question of whether counterfactuals in general should permit the substitution of rigidly coreferential terms is then raised. Having defended non-vacusim against Williamson’s objections, a range of arguments in its favour are considered.

Hyperintensionality

This chapter asks whether hyperintensionality is a genuine phenomenon, or rather, a feature to be explained away. It then focuses on the epistemic case, considering arguments from Stalnaker and Lewis which attempt to explain away hyperintensionality. The argument for a genuinely hyperintensional notion of content is subsequently considered. Having made the case for genuine hyperintensionality, the chapter turns to the granularity issue: how fine-grained are impossible worlds? This is one of the most difficult issues any theory of hyperintensionality faces. The focus then returns to the compositionality objection and it is argued that some accounts of impossible worlds deliver a fully compositional theory of meaning.

Epistemic Logics

Standard possible-worlds epistemic logic gives rise to the problem of logical omniscience. There are attempts to deal with the problem without using impossible worlds. A number of these approaches are discussed in this chapter and all are found wanting. The impossible worlds approach is immediately more successful, but faces a deep problem: how should impossible worlds be constrained, so as to give adequate models of knowledge and belief? One option is to take impossible worlds to be closed under some weaker-than-classical logic. But this approach does not genuinely solve the problem of logical omniscience. A different approach is the dynamic one, whereby epistemic states are not closed at any one time, but nevertheless evolve towards closure in a dynamic way.

Ersatz Modal Realism

Ersatz possible worlds can be understood as maximal states of affairs; maximal properties; recombinations of actual bits of reality; as maps; or as entities built from propositions or sentences. The question was: can these approaches be extended to include impossible worlds? The states of affairs approach can, with some modification, accommodate impossible worlds. The property approach too can, with some modification, be extended to impossible worlds. It is argued that the extended approach is best viewed as a form of linguistic ersatzism. The combinatorial faces the question: what are recombinations, metaphysically speaking? This approach collapses into one of the others. Map ersatzism does not seem general enough to accommodate all the impossibilities. The most promising approach is linguistic ersatzism. The chapter discusses an issue all ersatz accounts face: the problem of aliens.

From Possible to Impossible Worlds

Possible worlds are ways things might have been. They find applications in analysing possibility and necessity; propositions; knowledge and belief; information; and indicative and counterfactual conditionals. But possible worlds semantics faces the issue of hyperintensionality, generated by concepts that require distinctions between logical or necessary equivalents. The problems of distinguishing equivalent propositions, of logical omniscience, of information overload, of irrelevant conditionals, and of counterpossible conditionals, are all instances of the general issue. Adding impossible worlds promises to help with these puzzles. But can we genuinely think about the impossible? It is argued that we can.